Excellent question.
Bacteria of all sorts occurs naturally in and on living and dead things,
sometimes in a hibernating or stasis mode but in the tank you describe
it could take months for bacteria to populate. And the kind that would
populate would be just a few strains.
Coralline Algae would probably never appear in that tank, but....
The prevailing winds bring all kinds of marine algae and bacteria our
way from across the expanse of the Pacific Ocean. If that same tank were
placed outside where rain and dust would contaminate it, the time would
be shortened and the diversity would be quite interesting.
One of the major reasons that starting up a reef aquarium using some LS,
LR Macroalgae and LW from other hobbyists existing tanks is not only
for the thousands of different strains of bacteria, but for a myriad of
other bugs and worms that naturally live in our various systems.
Of course, Macroalgae has an extended important function because of how
it grows immediately and eats up pollution as fast as pollution is
produced by the recently moved LS, LR and new organic matter introduced
with clean base rock and sand.
Also, FYI, the bags of LS sold in the LFS are nowhere near as useful nor
do they have anywhere near the amount of bacteria of a single cup of LS
from a good aquarium. And they have no bugs and worms.